Problema Solution
quick computing company produces calculators. they have found that the cost, c(x), of making x calculators is a quadratic function in terms of x. the company also discovered that it cost $45 to produce 2 calculators, $143 to produce 4 calculators, and $869 to produce 10 calculators. find the total cost of producing 7 calculators
Answer provided by our tutors
c(x) = ax^2 + bx + c, where a, b, c are constants and a <> 0
c(2) = 45
a2^2 + 2b + c = 45
4a + 2b + c = 45
c(4) = 143
a4^2 + 4b + c = 143
16a + 4b + c = 143
c(10) = 869
a10^2 + 10b + c = 869
100a + 10b + c = 869
by solving the system of equations
4a + 2b + c = 45
16a + 4b + c = 143
100a + 10b + c = 869
we find
a = 9
b = -5
c = 19
click here to see the step by step solution of the system of equations
c(x) = 9x^2 + (-5)x + 19
c(x) = 9x^2 - 5x + 19
for x = 7 calculators we have
c(7) = 9*7^2 - 5*7 + 19
c(7) = $425
the total cost of producing 7 calculators is $425.